INVARIANT HILBERT SCHEMES AND DESINGULARIZATIONS OF QUOTIENTS BY CLASSICAL GROUPS

@article{Terpereau2013INVARIANTHS,
  title={INVARIANT HILBERT SCHEMES AND DESINGULARIZATIONS OF QUOTIENTS BY CLASSICAL GROUPS},
  author={Ronan Terpereau},
  journal={Transformation Groups},
  year={2013},
  volume={19},
  pages={247-281}
}
Let W be a finite-dimensional representation of a reductive algebraic group G. The invariant Hilbert scheme $$ \mathcal{H} $$ is a moduli space that classifies the G-stable closed subschemes Z of W such that the affine algebra k[Z] is the direct sum of simple G-modules with prescribed multiplicities. In this article, we consider the case where G is a classical group acting on a classical representation W and k[Z] is isomorphic to the regular representation of G as a G-module. We obtain families… CONTINUE READING